MAH-MHT CET (PCM/PCB) entrance exam Question Bank Solutions for Mathematics

If tan A – tan B = x and cot B – cot A = y, then cot(A – B) = ______.

sin 4θ can be written as ______.

A focus of an ellipse is at the origin. The directrix is the line x = 4 and the eccentricity is `1/2`. Then the length of the semi-major axis is ______.

If cos 2B = `(cos(A + C))/(cos(A - C))`, then tan A, tan B, tan C are in ______.

cos² 76° + cos² 16° – cos 76° cos 16° is equal to ______.

The value of `sin  π/16 sin  (3π)/16 sin  (5π)/16 sin  (7π)/16` is ______.

The value of cot 70° + 4 cos 70° is ______.

If A, B, C, D are the angles of a cyclic quadrilateral, then cos A + cos B + cos C + cos D is equal to ______.

If ABCD is a cyclic quadrilateral, then the value of cos A – cos B + cos C – cos D is equal to ______.

cos(36° − A) cos(36° + A) + cos(54° + A) cos(54° − A) = ______.

The equation of the plane passes through the point (2, 5, –3) perpendicular to the plane x + 2y + 2z = 1 and x – 2y + 3z = 4 is ______.

The differential equation of all circles passing through the origin and having their centres on the X-axis is ______.

`1/3(sqrt(3)  cos 23^circ -  sin 23^circ)` is equal to ______.

tan 57° – tan 12° – tan 57° tan 12° is equal to ______.

It is given that the events A and B are such that P(A) = `1/4, P(A/B) = 1/2` and `P(B/A) = 2/3`, then P(B) is equal to ______. 

The value of (cos α + cos β)² + (sin α + sin β)² is ______.

cos² x + cos² y – 2 cos x cos y cos (x + y) is equal to ______.

The value of tan 3A – tan 2A – tan A is ______.

The circles x² + y² + 6x + 6y = 0 and x² + y² – 12x –12y = 0

The differential equation of all parabolas having vertex at the origin and axis along positive Y-axis is ______.